TY - JOUR
AB - We establish the existence of a global solution for a new family of fluid-like equations, which are obtained in certain regimes in as the mean-field evolution of the supercurrent density in a (2D section of a) type-II superconductor with pinning and with imposed electric current. We also consider general vortex-sheet initial data, and investigate the uniqueness and regularity properties of the solution. For some choice of parameters, the equation under investigation coincides with the so-called lake equation from 2D shallow water fluid dynamics, and our analysis then leads to a new existence result for rough initial data.
AU - Duerinckx, Mitia
AU - Fischer, Julian L
ID - 606
IS - 5
JF - Annales de l'Institut Henri Poincare (C) Non Linear Analysis
TI - Well-posedness for mean-field evolutions arising in superconductivity
VL - 35
ER -